data-raw/data_backup.R
In XiaoruiZhu/parasol: Assessing the Partial Association Between Ordinal Variables
#' A list from an adjacent categories model
#'
#' This list contains dataset and model coefficients. This example is used to
#' illustrate the association between the residual variables when the
#' two ordinal variables Y1 and Y2 are partially independent. Data simulated from an
#' adjacent categories regression model with an ordered (preferably) factor response.
#' beta1 = 1, beta2 = -1,
#' alpha1 = (-Inf, -3, -2, 0, 2, 3, Inf), alpha2 = (-Inf, -2, 0, 2, Inf)
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 10000 rows and 11 variables.
#' \itemize{
#' \item \code{X} A continuous predictor variable.
#' \item \code{Y1} The response variable; an ordered factor.
#' \item \code{Y2} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang, Li, Shaobo, Yu, Yan, and Moustaki, Irini. Assessing partial association between
#' ordinal variables: quantification, visualization, and hypothesis testing, \emph{Journal of the
#' American Statistical Association}, Revision under review.
#'
#' @name df_AdjCat
#'
#' @usage
#' data(df_AdjCat)
#'
#' @examples
#' #
#' # Adjacent Categories Regression Model Example to compare different residuals.
#' # After adjusting covariates, the association between residuals variables should be independdent.
#' # Surrogate residuals has this property, whereas other types of residuals do not.
#' #
#'
#' data("df_AdjCat")
#' summary(df_AdjCat$data)
#' fit_clm1 <- VGAM::vglm(Y1 ~ X, family =
#' VGAM::cumulative(link = "logit",reverse=TRUE,parallel = TRUE),
#' data = df_AdjCat$data)
#' fit_clm2 <- VGAM::vglm(Y2 ~ X, family =
#' VGAM::cumulative(link = "logit",reverse=TRUE,parallel = TRUE),
#' data = df_AdjCat$data)
#' SR1 <- residuals(object = fit_clm1, type = "surrogate", surr.method = "latent", boot_id = NULL)
#' SR2 <- residuals(fit_clm2, type = "surrogate", surr.method = "latent", boot_id = NULL)
#'
#' ## obtain SBC residuals (Li and Shepherd 2012 JASA/Biometrika)
#' PR1 <- residuals(fit_clm1, type = "sign", boot_id = NULL)
#' PR2 <- residuals(fit_clm2, type = "sign", boot_id = NULL)
#'
#' ## obtain generalized residuals (Franses and Paap 2001 book)
#' GR1 <- residuals(fit_clm1, type = "general", boot_id = NULL)
#' GR2 <- residuals(fit_clm2, type = "general", boot_id = NULL)
#'
#' ## obtain deviance residuals
#' DR1 <- residuals(fit_clm1, type = "deviance", boot_id = NULL)
#' DR2 <- residuals(fit_clm2, type = "deviance", boot_id = NULL)
#'
#' ## visualize residual vs. residual
#' par(mfrow=c(2,2))
#' par(mar=c(4, 4.8, 2.5, 1.5))
#'
#' plot(PR1, PR2, pch=".", main = "sign-based Residuals",
#' xlab = expression(paste(R[1]^"ALT")),
#' ylab = expression(paste(R[2]^"ALT")))
#' plot(GR1, GR2, pch=".", main = "generalized Residuals",
#' xlab = expression(paste(R[1]^"ALT")),
#' ylab = expression(paste(R[2]^"ALT")), xlim = c(-4,4), ylim=c(-4,4))
#' plot(DR1, DR2, pch='.', main = "deviance Residuals",
#' xlab = expression(paste(R[1]^"ALT")),
#' ylab = expression(paste(R[2]^"ALT")))
#' plot(SR1, SR2, pch=".", main = "Surrogate Residuals", xaxt="n", yaxt="n",
#' xlab = expression(R[1]), ylab = expression(R[2]),
#' xlim = c(-1/2,1/2), ylim=c(-1/2,1/2))
#' axis(1, at=seq(-0.5, 0.5, 0.25), labels = seq(-0.5, 0.5, 0.25))
#' axis(2, at=seq(-0.5, 0.5, 0.25), labels = seq(-0.5, 0.5, 0.25))
#'
NULL
#' Raw dataset of US 2016 national election study
#'
#' A subset of the 2016 American National Election Study.
#' Pre-election preference is recorded as "IntendVote", while the actual vote is "voteResult".
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 4271 rows and 12 variables.
#' \itemize{
#' \item \code{WeightforPreElection} Pre-election weight of a respondent.
#'
#' \item \code{WeightforPostElection} Post-election weight of a respondent.
#'
#' \item \code{selfLR} Left-Right self-placement of respondent: an ordered
#' factor with levels \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): an ordered factor with levels \code{extLib} <
#' \code{Lib} < \code{sliLib} < \code{Mod} < \code{sliCon} <
#' \code{Con} < \code{extCon}.
#'
#' \item \code{PID} Party identification: an ordered factor with levels strong
#' Democrat, \code{strDem} < weak Democrat, \code{weakDem} < independent Democrat,
#' \code{indDem} < independent independent \code{indind} < indepedent Republican,
#' \code{indRep} < weak Republican, \code{weakRep} < strong Republican, \code{strRep}.
#'
#' \item \code{agegroup} Respondent's age category.
#'
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{educ} Respondent's education category: an ordered factor with levels
#' 8 years or less, \code{MS} < high school dropout, \code{HSdrop} < high school
#' diploma or GED, \code{HS} < some College, \code{Coll} < Community or junior
#' College degree, \code{CCdeg} < BA degree, \code{BAdeg} < postgraduate degree,
#' \code{MAdeg}.
#'
#' \item \code{income} Categorical variable representing the Respondent's family income
#'
#' \item \code{income.num} Respondent's family income in thousands: an numerical variable.
#' income.num = recode(income, '(01) 01. Under $5,000' = 5, '(02) 02. $5,000-$9,999' = 7.5,
#' '(03) 03. $10,000-$12,499' = 11.25, '(04) 04. $12,500-$14,999' = 13.75,
#' '(05) 05. $15,000-$17,499' = 16.25, '(06) 06. $17,500-$19,999' = 18.75,
#' '(07) 07. $20,000-$22,499' = 21.25, '(08) 08. $22,500-$24,999' = 23.75,
#' '(09) 09. $25,000-$27,499' = 26.25, '(10) 10. $27,500-$29,999' = 28.75,
#' '(11) 11. $30,000-$34,999' = 32.5, '(12) 12. $35,000-$39,999' = 37.5,
#' '(13) 13. $40,000-$44,999' = 42.5, '(14) 14. $45,000-$49,999' = 47.5,
#' '(15) 15. $50,000-$54,999' = 52.5, '(16) 16. $55,000-$59,999' = 57.5,
#' '(17) 17. $60,000-$64,999' = 62.5, '(18) 18. $65,000-$69,999' = 67.5,
#' '(19) 19. $70,000-$74,999' = 72.5, '(20) 20. $75,000-$79,999' = 77.5,
#' '(21) 21. $80,000-$89,999' = 85, '(22) 22. $90,000-$99,999' = 95,
#' '(23) 23. $100,000-$109,999' = 105, '(24) 24. $110,000-$124,999' = 117.5,
#' '(25) 25. $125,000-$149,999' = 137.5, '(26) 26. $150,000-$174,999' = 162.5,
#' '(27) 27. $175,000-$249,999' = 212.5, '(28) 28. $250,000 or more' = 250)
#'
#' \item \code{IntendVote} The intend vote two months preceeding the
#' November election (Pre-election interview). It is a factor with levels
#' \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Prevote.num} Recode the intend vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{voteResult} The actual vote answered in the interview during the
#' two months following the election (Post-election interview). It is a factor
#' with levels \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Postvote.num} Recode the actual vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#' }
#'
#'
#' @name nes2016_raw
#'
#' @usage
#' data(nes2016_raw)
#'
#' @examples
#' head(nes2016_raw)
NULL
#' US 2016 national election study with pre-election interview only (Clean)
#'
#' A subset of the 2016 American National Election Study.
#' The Pre-election preference is recorded as "IntendVote" and the "Prevote.num"
#' is the numeric of it. Observations with missing values, or "No thought"
#' responses have been removed. Responsdents expressing a voting preference
#' other than Clinton or Trump have been removed.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2188 rows and 10 variables.
#' \itemize{
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{edu.year} Respondent's education year, which is mapped from raw data
#' \code{nes2016_raw}. \code{MS}=8, \code{HSdrop}=11, \code{HS}=12, \code{Coll}=14,
#' \code{CCdeg}=15, \code{BAdeg}=17, \code{MAdeg}=19.
#'
#' \item \code{income.num} Respondent's family income in thousands: an numerical variable.
#' income.num = recode(income, '(01) 01. Under $5,000' = 5, '(02) 02. $5,000-$9,999' = 7.5,
#' '(03) 03. $10,000-$12,499' = 11.25, '(04) 04. $12,500-$14,999' = 13.75,
#' '(05) 05. $15,000-$17,499' = 16.25, '(06) 06. $17,500-$19,999' = 18.75,
#' '(07) 07. $20,000-$22,499' = 21.25, '(08) 08. $22,500-$24,999' = 23.75,
#' '(09) 09. $25,000-$27,499' = 26.25, '(10) 10. $27,500-$29,999' = 28.75,
#' '(11) 11. $30,000-$34,999' = 32.5, '(12) 12. $35,000-$39,999' = 37.5,
#' '(13) 13. $40,000-$44,999' = 42.5, '(14) 14. $45,000-$49,999' = 47.5,
#' '(15) 15. $50,000-$54,999' = 52.5, '(16) 16. $55,000-$59,999' = 57.5,
#' '(17) 17. $60,000-$64,999' = 62.5, '(18) 18. $65,000-$69,999' = 67.5,
#' '(19) 19. $70,000-$74,999' = 72.5, '(20) 20. $75,000-$79,999' = 77.5,
#' '(21) 21. $80,000-$89,999' = 85, '(22) 22. $90,000-$99,999' = 95,
#' '(23) 23. $100,000-$109,999' = 105, '(24) 24. $110,000-$124,999' = 117.5,
#' '(25) 25. $125,000-$149,999' = 137.5, '(26) 26. $150,000-$174,999' = 162.5,
#' '(27) 27. $175,000-$249,999' = 212.5, '(28) 28. $250,000 or more' = 250)
#'
#' \item \code{PID} Party identification: a numeric variable with value from 1 to 7
#' representing strong Democrat, \code{strDem} < weak Democrat, \code{weakDem} <
#' independent Democrat, \code{indDem} < independent independent \code{indind} <
#' indepedent Republican, \code{indRep} < weak Republican, \code{weakRep} <
#' strong Republican, \code{strRep}.
#' \item \code{selfLR} Left-Right self-placement of respondent: a numeric variable
#' with value from 1 to 7 representing \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{TrumpLR} Left-Right placement of Donald Trump (same
#' scale as selfLR), a numeric variable with value from 1 to 7.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): a numeric variable with value from 1 to 7.
#'
#' \item \code{IntendVote} The intend vote two months preceeding the
#' November election (Pre-election interview). It is a factor with levels
#' \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Prevote.num} Recode the intend vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{WeightforPreElection} Pre-election weight of a respondent.
#'
#' }
#'
#'
#' @name nes2016_pre
#'
#' @usage
#' data(nes2016_pre)
#'
#' @examples
#' head(nes2016_pre)
NULL
#' US 2016 national election study with post-election interview only (Clean)
#'
#' A subset of the 2016 American National Election Study. The actual vote is "voteResult".
#' "Postvote.num" is recoded variable of "voteResult". Observations with missing values,
#' or "No thought" responses have been removed. Responsdents expressing
#' a voting preference other than Clinton or Trump have been removed.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 1892 rows and 10 variables.
#' \itemize{
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{edu.year} Respondent's education year, which is mapped from raw data
#' \code{nes2016_raw}. \code{MS}=8, \code{HSdrop}=11, \code{HS}=12, \code{Coll}=14,
#' \code{CCdeg}=15, \code{BAdeg}=17, \code{MAdeg}=19.
#'
#' \item \code{income.num} Respondent's family income in thousands: an numerical variable.
#'
#' \item \code{PID} Party identification: a numeric variable with value from 1 to 7
#' representing strong Democrat, \code{strDem} < weak Democrat, \code{weakDem} <
#' independent Democrat, \code{indDem} < independent independent \code{indind} <
#' indepedent Republican, \code{indRep} < weak Republican, \code{weakRep} <
#' strong Republican, \code{strRep}.
#' \item \code{selfLR} Left-Right self-placement of respondent: a numeric variable
#' with value from 1 to 7 representing \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{TrumpLR} Left-Right placement of Donald Trump (same
#' scale as selfLR), a numeric variable with value from 1 to 7.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): a numeric variable with value from 1 to 7.
#'
#' \item \code{voteResult} The actual vote answered in the interview during the
#' two months following the election (Post-election interview). It is a factor
#' with levels \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Postvote.num} Recode the actual vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{WeightforPostElection} Post-election weight of a respondent.
#'
#' }
#'
#'
#' @name nes2016_post
#'
#' @usage
#' data(nes2016_post)
#'
#' @examples
#' head(nes2016_post)
NULL
#' US 2016 national election study of respondents in both pre-election and post-election interviews (Clean)
#'
#' A subset of the 2016 American National Election Study. Pre-election preference is recorded
#' as "IntendVote", while the actual vote is "voteResult".
#' "Prevote.num" and "Postvote.num" are the numeric for them, respectively. Observations
#' with missing values, or "No thought" responses have been removed. Responsdents expressing
#' a voting preference other than Clinton or Trump have been removed.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 1690 rows and 14 variables.
#' \itemize{
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{edu.year} Respondent's education year, which is mapped from raw data
#' \code{nes2016_raw}. \code{MS}=8, \code{HSdrop}=11, \code{HS}=12, \code{Coll}=14,
#' \code{CCdeg}=15, \code{BAdeg}=17, \code{MAdeg}=19.
#'
#' \item \code{income.num} Respondent's family income in thousands: an numerical variable.
#'
#' \item \code{PID} Party identification: a numeric variable with value from 1 to 7
#' representing strong Democrat, \code{strDem} < weak Democrat, \code{weakDem} <
#' independent Democrat, \code{indDem} < independent independent \code{indind} <
#' indepedent Republican, \code{indRep} < weak Republican, \code{weakRep} <
#' strong Republican, \code{strRep}.
#' \item \code{selfLR} Left-Right self-placement of respondent: a numeric variable
#' with value from 1 to 7 representing \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{TrumpLR} Left-Right placement of Donald Trump (same
#' scale as selfLR), a numeric variable with value from 1 to 7.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): a numeric variable with value from 1 to 7.
#'
#' \item \code{IntendVote} The intend vote two months preceeding the
#' November election (Pre-election interview). It is a factor with levels
#' \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Prevote.num} Recode the intend vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{voteResult} The actual vote answered in the interview during the
#' two months following the election (Post-election interview). It is a factor
#' with levels \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Postvote.num} Recode the actual vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{WeightforPreElection} Pre-election weight of a respondent.
#'
#' \item \code{WeightforPostElection} Post-election weight of a respondent.
#'
#' }
#'
#'
#' @name nes2016_prepost
#'
#' @usage
#' data(nes2016_prepost)
#'
#' @examples
#' head(nes2016_prepost)
NULL
#' US 1996 national election study
#'
#' A data with 13 variables subset of the 1996 American National Election Study.
#' The data has been cleaned, and a few numeric variables are added.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 944 rows and 13 variables.
#' \itemize{
#' \item \code{popul} population of respondent's location in 1000s of people.
#'
#' \item \code{TVnews} days in the past week spent watching news on TV.
#'
#' \item \code{selfLR} Left-Right self-placement of respondent: an ordered
#' factor with levels \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): an ordered factor with levels \code{extLib} <
#' \code{Lib} < \code{sliLib} < \code{Mod} < \code{sliCon} <
#' \code{Con} < \code{extCon}.
#'
#' \item \code{PID} Party identification.
#'
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{educ} Respondent's education,
#'
#' \item \code{edu.year} Respondent's education (Recoded), edu.year=
#' recode(educ, 'MS'=8, 'HSdrop'=11, 'HS'=12, 'Coll'=14, 'CCdeg'=15,
#' 'BAdeg'=17, 'MAdeg'=19).
#'
#' \item \code{income} Respondent's family income
#'
#' \item \code{income.num} Respondent's family income: an ordered
#' factor with levels: income.num=recode(income, '3Kminus'=3, '3K-5K'=4,
#' '5K-7K'=6, '7K-9K'=8, '9K-10K'=9.5, '10K-11K'=10.5,
#' '11K-12K'=11.5, '12K-13K'=12.5, '13K-14K'=13.5, '14K-15K'=14.5,
#' '15K-17K'=16, '17K-20K'=18.5, '20K-22K'=21, '22K-25K'=23.5,
#' '25K-30K'=27.5, '30K-35K'=32.5, '35K-40K'=37.5, '40K-45K'=42.5,
#' '45K-50K'=47.5, '50K-60K'=55, '60K-75K'=67, '75K-90K'=80,
#' '90K-105K'=95, '105Kplus'=105).
#'
#' \item \code{vote} Expected vote in 1996 presidential election:
#' a factor with levels \code{Clinton} and \code{Dole}.
#'
#' \item \code{vote.num} recode(vote, 'Clinton'=0, 'Dole'=1),
#' }
#'
#'
#' @name nes96
#'
#' @usage
#' data(nes96)
#'
#' @examples
#' head(nes96)
NULL
#' Simulated quadratic data
#'
#' Data simulated from a probit model with a quadratic trend. The data are
#' described in Example 2 of Liu and Zhang (2017).
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2000 rows and 2 variables.
#' \itemize{
#' \item \code{x} The predictor variable.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df1
#'
#' @usage
#' data(df1)
#'
#' @examples
#' head(df1)
NULL
#' Simulated heteroscedastic data
#'
#' Data simulated from a probit model with heteroscedasticity. The data are
#' described in Example 4 of Liu and Zhang (2017).
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2000 rows and 2 variables.
#' \itemize{
#' \item \code{x} The predictor variable.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df2
#'
#' @usage
#' data(df2)
#'
#' @examples
#' head(df2)
NULL
#' Simulated Gumbel data
#'
#' Data simulated from a log-log model with a quadratic trend. The data are
#' described in Example 3 of Liu and Zhang (2017).
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2000 rows and 2 variables.
#' \itemize{
#' \item \code{x} The predictor variable.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df3
#'
#' @usage
#' data(df3)
#'
#' @examples
#' head(df3)
NULL
#' Simulated proportionality data
#'
#' Data simulated from from two separate probit models. The data are described
#' in Example 5 of Liu and Zhang (2017).
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 4000 rows and 2 variables.
#' \itemize{
#' \item \code{x} The predictor variable.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df4
#'
#' @usage
#' data(df4)
#'
#' @examples
#' head(df4)
NULL
#' Simulated interaction data
#'
#' Data simulated from from an ordered probit model with an interaction effect.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2000 rows and 3 variables.
#' \itemize{
#' \item \code{x1} A continuous predictor variable.
#' \item \code{x2} A factor with two levels: \code{"Control"} and
#' \code{"Treatment"}.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df5
#'
#' @usage
#' data(df5)
#'
#' @examples
#' head(df5)
NULL
XiaoruiZhu/parasol documentation built on Feb. 12, 2024, 7:34 a.m.
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#' A list from an adjacent categories model
#'
#' This list contains dataset and model coefficients. This example is used to
#' illustrate the association between the residual variables when the
#' two ordinal variables Y1 and Y2 are partially independent. Data simulated from an
#' adjacent categories regression model with an ordered (preferably) factor response.
#' beta1 = 1, beta2 = -1,
#' alpha1 = (-Inf, -3, -2, 0, 2, 3, Inf), alpha2 = (-Inf, -2, 0, 2, Inf)
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 10000 rows and 11 variables.
#' \itemize{
#' \item \code{X} A continuous predictor variable.
#' \item \code{Y1} The response variable; an ordered factor.
#' \item \code{Y2} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang, Li, Shaobo, Yu, Yan, and Moustaki, Irini. Assessing partial association between
#' ordinal variables: quantification, visualization, and hypothesis testing, \emph{Journal of the
#' American Statistical Association}, Revision under review.
#'
#' @name df_AdjCat
#'
#' @usage
#' data(df_AdjCat)
#'
#' @examples
#' #
#' # Adjacent Categories Regression Model Example to compare different residuals.
#' # After adjusting covariates, the association between residuals variables should be independdent.
#' # Surrogate residuals has this property, whereas other types of residuals do not.
#' #
#'
#' data("df_AdjCat")
#' summary(df_AdjCat$data)
#' fit_clm1 <- VGAM::vglm(Y1 ~ X, family =
#' VGAM::cumulative(link = "logit",reverse=TRUE,parallel = TRUE),
#' data = df_AdjCat$data)
#' fit_clm2 <- VGAM::vglm(Y2 ~ X, family =
#' VGAM::cumulative(link = "logit",reverse=TRUE,parallel = TRUE),
#' data = df_AdjCat$data)
#' SR1 <- residuals(object = fit_clm1, type = "surrogate", surr.method = "latent", boot_id = NULL)
#' SR2 <- residuals(fit_clm2, type = "surrogate", surr.method = "latent", boot_id = NULL)
#'
#' ## obtain SBC residuals (Li and Shepherd 2012 JASA/Biometrika)
#' PR1 <- residuals(fit_clm1, type = "sign", boot_id = NULL)
#' PR2 <- residuals(fit_clm2, type = "sign", boot_id = NULL)
#'
#' ## obtain generalized residuals (Franses and Paap 2001 book)
#' GR1 <- residuals(fit_clm1, type = "general", boot_id = NULL)
#' GR2 <- residuals(fit_clm2, type = "general", boot_id = NULL)
#'
#' ## obtain deviance residuals
#' DR1 <- residuals(fit_clm1, type = "deviance", boot_id = NULL)
#' DR2 <- residuals(fit_clm2, type = "deviance", boot_id = NULL)
#'
#' ## visualize residual vs. residual
#' par(mfrow=c(2,2))
#' par(mar=c(4, 4.8, 2.5, 1.5))
#'
#' plot(PR1, PR2, pch=".", main = "sign-based Residuals",
#' xlab = expression(paste(R[1]^"ALT")),
#' ylab = expression(paste(R[2]^"ALT")))
#' plot(GR1, GR2, pch=".", main = "generalized Residuals",
#' xlab = expression(paste(R[1]^"ALT")),
#' ylab = expression(paste(R[2]^"ALT")), xlim = c(-4,4), ylim=c(-4,4))
#' plot(DR1, DR2, pch='.', main = "deviance Residuals",
#' xlab = expression(paste(R[1]^"ALT")),
#' ylab = expression(paste(R[2]^"ALT")))
#' plot(SR1, SR2, pch=".", main = "Surrogate Residuals", xaxt="n", yaxt="n",
#' xlab = expression(R[1]), ylab = expression(R[2]),
#' xlim = c(-1/2,1/2), ylim=c(-1/2,1/2))
#' axis(1, at=seq(-0.5, 0.5, 0.25), labels = seq(-0.5, 0.5, 0.25))
#' axis(2, at=seq(-0.5, 0.5, 0.25), labels = seq(-0.5, 0.5, 0.25))
#'
NULL
#' Raw dataset of US 2016 national election study
#'
#' A subset of the 2016 American National Election Study.
#' Pre-election preference is recorded as "IntendVote", while the actual vote is "voteResult".
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 4271 rows and 12 variables.
#' \itemize{
#' \item \code{WeightforPreElection} Pre-election weight of a respondent.
#'
#' \item \code{WeightforPostElection} Post-election weight of a respondent.
#'
#' \item \code{selfLR} Left-Right self-placement of respondent: an ordered
#' factor with levels \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): an ordered factor with levels \code{extLib} <
#' \code{Lib} < \code{sliLib} < \code{Mod} < \code{sliCon} <
#' \code{Con} < \code{extCon}.
#'
#' \item \code{PID} Party identification: an ordered factor with levels strong
#' Democrat, \code{strDem} < weak Democrat, \code{weakDem} < independent Democrat,
#' \code{indDem} < independent independent \code{indind} < indepedent Republican,
#' \code{indRep} < weak Republican, \code{weakRep} < strong Republican, \code{strRep}.
#'
#' \item \code{agegroup} Respondent's age category.
#'
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{educ} Respondent's education category: an ordered factor with levels
#' 8 years or less, \code{MS} < high school dropout, \code{HSdrop} < high school
#' diploma or GED, \code{HS} < some College, \code{Coll} < Community or junior
#' College degree, \code{CCdeg} < BA degree, \code{BAdeg} < postgraduate degree,
#' \code{MAdeg}.
#'
#' \item \code{income} Categorical variable representing the Respondent's family income
#'
#' \item \code{income.num} Respondent's family income in thousands: an numerical variable.
#' income.num = recode(income, '(01) 01. Under $5,000' = 5, '(02) 02. $5,000-$9,999' = 7.5,
#' '(03) 03. $10,000-$12,499' = 11.25, '(04) 04. $12,500-$14,999' = 13.75,
#' '(05) 05. $15,000-$17,499' = 16.25, '(06) 06. $17,500-$19,999' = 18.75,
#' '(07) 07. $20,000-$22,499' = 21.25, '(08) 08. $22,500-$24,999' = 23.75,
#' '(09) 09. $25,000-$27,499' = 26.25, '(10) 10. $27,500-$29,999' = 28.75,
#' '(11) 11. $30,000-$34,999' = 32.5, '(12) 12. $35,000-$39,999' = 37.5,
#' '(13) 13. $40,000-$44,999' = 42.5, '(14) 14. $45,000-$49,999' = 47.5,
#' '(15) 15. $50,000-$54,999' = 52.5, '(16) 16. $55,000-$59,999' = 57.5,
#' '(17) 17. $60,000-$64,999' = 62.5, '(18) 18. $65,000-$69,999' = 67.5,
#' '(19) 19. $70,000-$74,999' = 72.5, '(20) 20. $75,000-$79,999' = 77.5,
#' '(21) 21. $80,000-$89,999' = 85, '(22) 22. $90,000-$99,999' = 95,
#' '(23) 23. $100,000-$109,999' = 105, '(24) 24. $110,000-$124,999' = 117.5,
#' '(25) 25. $125,000-$149,999' = 137.5, '(26) 26. $150,000-$174,999' = 162.5,
#' '(27) 27. $175,000-$249,999' = 212.5, '(28) 28. $250,000 or more' = 250)
#'
#' \item \code{IntendVote} The intend vote two months preceeding the
#' November election (Pre-election interview). It is a factor with levels
#' \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Prevote.num} Recode the intend vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{voteResult} The actual vote answered in the interview during the
#' two months following the election (Post-election interview). It is a factor
#' with levels \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Postvote.num} Recode the actual vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#' }
#'
#'
#' @name nes2016_raw
#'
#' @usage
#' data(nes2016_raw)
#'
#' @examples
#' head(nes2016_raw)
NULL
#' US 2016 national election study with pre-election interview only (Clean)
#'
#' A subset of the 2016 American National Election Study.
#' The Pre-election preference is recorded as "IntendVote" and the "Prevote.num"
#' is the numeric of it. Observations with missing values, or "No thought"
#' responses have been removed. Responsdents expressing a voting preference
#' other than Clinton or Trump have been removed.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2188 rows and 10 variables.
#' \itemize{
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{edu.year} Respondent's education year, which is mapped from raw data
#' \code{nes2016_raw}. \code{MS}=8, \code{HSdrop}=11, \code{HS}=12, \code{Coll}=14,
#' \code{CCdeg}=15, \code{BAdeg}=17, \code{MAdeg}=19.
#'
#' \item \code{income.num} Respondent's family income in thousands: an numerical variable.
#' income.num = recode(income, '(01) 01. Under $5,000' = 5, '(02) 02. $5,000-$9,999' = 7.5,
#' '(03) 03. $10,000-$12,499' = 11.25, '(04) 04. $12,500-$14,999' = 13.75,
#' '(05) 05. $15,000-$17,499' = 16.25, '(06) 06. $17,500-$19,999' = 18.75,
#' '(07) 07. $20,000-$22,499' = 21.25, '(08) 08. $22,500-$24,999' = 23.75,
#' '(09) 09. $25,000-$27,499' = 26.25, '(10) 10. $27,500-$29,999' = 28.75,
#' '(11) 11. $30,000-$34,999' = 32.5, '(12) 12. $35,000-$39,999' = 37.5,
#' '(13) 13. $40,000-$44,999' = 42.5, '(14) 14. $45,000-$49,999' = 47.5,
#' '(15) 15. $50,000-$54,999' = 52.5, '(16) 16. $55,000-$59,999' = 57.5,
#' '(17) 17. $60,000-$64,999' = 62.5, '(18) 18. $65,000-$69,999' = 67.5,
#' '(19) 19. $70,000-$74,999' = 72.5, '(20) 20. $75,000-$79,999' = 77.5,
#' '(21) 21. $80,000-$89,999' = 85, '(22) 22. $90,000-$99,999' = 95,
#' '(23) 23. $100,000-$109,999' = 105, '(24) 24. $110,000-$124,999' = 117.5,
#' '(25) 25. $125,000-$149,999' = 137.5, '(26) 26. $150,000-$174,999' = 162.5,
#' '(27) 27. $175,000-$249,999' = 212.5, '(28) 28. $250,000 or more' = 250)
#'
#' \item \code{PID} Party identification: a numeric variable with value from 1 to 7
#' representing strong Democrat, \code{strDem} < weak Democrat, \code{weakDem} <
#' independent Democrat, \code{indDem} < independent independent \code{indind} <
#' indepedent Republican, \code{indRep} < weak Republican, \code{weakRep} <
#' strong Republican, \code{strRep}.
#' \item \code{selfLR} Left-Right self-placement of respondent: a numeric variable
#' with value from 1 to 7 representing \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{TrumpLR} Left-Right placement of Donald Trump (same
#' scale as selfLR), a numeric variable with value from 1 to 7.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): a numeric variable with value from 1 to 7.
#'
#' \item \code{IntendVote} The intend vote two months preceeding the
#' November election (Pre-election interview). It is a factor with levels
#' \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Prevote.num} Recode the intend vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{WeightforPreElection} Pre-election weight of a respondent.
#'
#' }
#'
#'
#' @name nes2016_pre
#'
#' @usage
#' data(nes2016_pre)
#'
#' @examples
#' head(nes2016_pre)
NULL
#' US 2016 national election study with post-election interview only (Clean)
#'
#' A subset of the 2016 American National Election Study. The actual vote is "voteResult".
#' "Postvote.num" is recoded variable of "voteResult". Observations with missing values,
#' or "No thought" responses have been removed. Responsdents expressing
#' a voting preference other than Clinton or Trump have been removed.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 1892 rows and 10 variables.
#' \itemize{
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{edu.year} Respondent's education year, which is mapped from raw data
#' \code{nes2016_raw}. \code{MS}=8, \code{HSdrop}=11, \code{HS}=12, \code{Coll}=14,
#' \code{CCdeg}=15, \code{BAdeg}=17, \code{MAdeg}=19.
#'
#' \item \code{income.num} Respondent's family income in thousands: an numerical variable.
#'
#' \item \code{PID} Party identification: a numeric variable with value from 1 to 7
#' representing strong Democrat, \code{strDem} < weak Democrat, \code{weakDem} <
#' independent Democrat, \code{indDem} < independent independent \code{indind} <
#' indepedent Republican, \code{indRep} < weak Republican, \code{weakRep} <
#' strong Republican, \code{strRep}.
#' \item \code{selfLR} Left-Right self-placement of respondent: a numeric variable
#' with value from 1 to 7 representing \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{TrumpLR} Left-Right placement of Donald Trump (same
#' scale as selfLR), a numeric variable with value from 1 to 7.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): a numeric variable with value from 1 to 7.
#'
#' \item \code{voteResult} The actual vote answered in the interview during the
#' two months following the election (Post-election interview). It is a factor
#' with levels \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Postvote.num} Recode the actual vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{WeightforPostElection} Post-election weight of a respondent.
#'
#' }
#'
#'
#' @name nes2016_post
#'
#' @usage
#' data(nes2016_post)
#'
#' @examples
#' head(nes2016_post)
NULL
#' US 2016 national election study of respondents in both pre-election and post-election interviews (Clean)
#'
#' A subset of the 2016 American National Election Study. Pre-election preference is recorded
#' as "IntendVote", while the actual vote is "voteResult".
#' "Prevote.num" and "Postvote.num" are the numeric for them, respectively. Observations
#' with missing values, or "No thought" responses have been removed. Responsdents expressing
#' a voting preference other than Clinton or Trump have been removed.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 1690 rows and 14 variables.
#' \itemize{
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{edu.year} Respondent's education year, which is mapped from raw data
#' \code{nes2016_raw}. \code{MS}=8, \code{HSdrop}=11, \code{HS}=12, \code{Coll}=14,
#' \code{CCdeg}=15, \code{BAdeg}=17, \code{MAdeg}=19.
#'
#' \item \code{income.num} Respondent's family income in thousands: an numerical variable.
#'
#' \item \code{PID} Party identification: a numeric variable with value from 1 to 7
#' representing strong Democrat, \code{strDem} < weak Democrat, \code{weakDem} <
#' independent Democrat, \code{indDem} < independent independent \code{indind} <
#' indepedent Republican, \code{indRep} < weak Republican, \code{weakRep} <
#' strong Republican, \code{strRep}.
#' \item \code{selfLR} Left-Right self-placement of respondent: a numeric variable
#' with value from 1 to 7 representing \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{TrumpLR} Left-Right placement of Donald Trump (same
#' scale as selfLR), a numeric variable with value from 1 to 7.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): a numeric variable with value from 1 to 7.
#'
#' \item \code{IntendVote} The intend vote two months preceeding the
#' November election (Pre-election interview). It is a factor with levels
#' \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Prevote.num} Recode the intend vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{voteResult} The actual vote answered in the interview during the
#' two months following the election (Post-election interview). It is a factor
#' with levels \code{HillaryClinton} and \code{DonaldTrump}.
#'
#' \item \code{Postvote.num} Recode the actual vote to numeric values,
#' 'HillaryClinton'=0, 'DonaldTrump'=1.
#'
#' \item \code{WeightforPreElection} Pre-election weight of a respondent.
#'
#' \item \code{WeightforPostElection} Post-election weight of a respondent.
#'
#' }
#'
#'
#' @name nes2016_prepost
#'
#' @usage
#' data(nes2016_prepost)
#'
#' @examples
#' head(nes2016_prepost)
NULL
#' US 1996 national election study
#'
#' A data with 13 variables subset of the 1996 American National Election Study.
#' The data has been cleaned, and a few numeric variables are added.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 944 rows and 13 variables.
#' \itemize{
#' \item \code{popul} population of respondent's location in 1000s of people.
#'
#' \item \code{TVnews} days in the past week spent watching news on TV.
#'
#' \item \code{selfLR} Left-Right self-placement of respondent: an ordered
#' factor with levels \code{extLib}: extremely liberal, \code{Lib}: liberal,
#' \code{sliLib}: slightly liberal, \code{Mod}: moderate, \code{sliCon}:
#' slightly conservative, \code{Con}: conservative, \code{extCon}: extremely
#' conservative. \code{extLib} < \code{Lib} < \code{sliLib} <
#' \code{Mod} < \code{sliCon} < \code{Con} < \code{extCon}.
#'
#' \item \code{ClinLR} Left-Right placement of Bill Clinton (same
#' scale as selfLR): an ordered factor with levels \code{extLib} <
#' \code{Lib} < \code{sliLib} < \code{Mod} < \code{sliCon} <
#' \code{Con} < \code{extCon}.
#'
#' \item \code{PID} Party identification.
#'
#' \item \code{age} Respondent's age in years.
#'
#' \item \code{educ} Respondent's education,
#'
#' \item \code{edu.year} Respondent's education (Recoded), edu.year=
#' recode(educ, 'MS'=8, 'HSdrop'=11, 'HS'=12, 'Coll'=14, 'CCdeg'=15,
#' 'BAdeg'=17, 'MAdeg'=19).
#'
#' \item \code{income} Respondent's family income
#'
#' \item \code{income.num} Respondent's family income: an ordered
#' factor with levels: income.num=recode(income, '3Kminus'=3, '3K-5K'=4,
#' '5K-7K'=6, '7K-9K'=8, '9K-10K'=9.5, '10K-11K'=10.5,
#' '11K-12K'=11.5, '12K-13K'=12.5, '13K-14K'=13.5, '14K-15K'=14.5,
#' '15K-17K'=16, '17K-20K'=18.5, '20K-22K'=21, '22K-25K'=23.5,
#' '25K-30K'=27.5, '30K-35K'=32.5, '35K-40K'=37.5, '40K-45K'=42.5,
#' '45K-50K'=47.5, '50K-60K'=55, '60K-75K'=67, '75K-90K'=80,
#' '90K-105K'=95, '105Kplus'=105).
#'
#' \item \code{vote} Expected vote in 1996 presidential election:
#' a factor with levels \code{Clinton} and \code{Dole}.
#'
#' \item \code{vote.num} recode(vote, 'Clinton'=0, 'Dole'=1),
#' }
#'
#'
#' @name nes96
#'
#' @usage
#' data(nes96)
#'
#' @examples
#' head(nes96)
NULL
#' Simulated quadratic data
#'
#' Data simulated from a probit model with a quadratic trend. The data are
#' described in Example 2 of Liu and Zhang (2017).
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2000 rows and 2 variables.
#' \itemize{
#' \item \code{x} The predictor variable.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df1
#'
#' @usage
#' data(df1)
#'
#' @examples
#' head(df1)
NULL
#' Simulated heteroscedastic data
#'
#' Data simulated from a probit model with heteroscedasticity. The data are
#' described in Example 4 of Liu and Zhang (2017).
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2000 rows and 2 variables.
#' \itemize{
#' \item \code{x} The predictor variable.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df2
#'
#' @usage
#' data(df2)
#'
#' @examples
#' head(df2)
NULL
#' Simulated Gumbel data
#'
#' Data simulated from a log-log model with a quadratic trend. The data are
#' described in Example 3 of Liu and Zhang (2017).
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2000 rows and 2 variables.
#' \itemize{
#' \item \code{x} The predictor variable.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df3
#'
#' @usage
#' data(df3)
#'
#' @examples
#' head(df3)
NULL
#' Simulated proportionality data
#'
#' Data simulated from from two separate probit models. The data are described
#' in Example 5 of Liu and Zhang (2017).
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 4000 rows and 2 variables.
#' \itemize{
#' \item \code{x} The predictor variable.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df4
#'
#' @usage
#' data(df4)
#'
#' @examples
#' head(df4)
NULL
#' Simulated interaction data
#'
#' Data simulated from from an ordered probit model with an interaction effect.
#'
#' @docType data
#'
#' @keywords datasets
#'
#' @format A data frame with 2000 rows and 3 variables.
#' \itemize{
#' \item \code{x1} A continuous predictor variable.
#' \item \code{x2} A factor with two levels: \code{"Control"} and
#' \code{"Treatment"}.
#' \item \code{y} The response variable; an ordered factor.
#' }
#'
#' @references
#' Liu, Dungang and Zhang, Heping. Residuals and Diagnostics for Ordinal
#' Regression Models: A Surrogate Approach.
#' \emph{Journal of the American Statistical Association} (accepted).
#'
#' @name df5
#'
#' @usage
#' data(df5)
#'
#' @examples
#' head(df5)
NULL
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